Article ID: CBB619659341

Zur Einführung einer begrifflichen Perspektive in die Mathematik: Dedekind, Noether, van der Waerden (2015)

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For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden. „She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine – of all that is characterized by the term ‚Begriffliche Mathematik‘.“2 The aim of this paper is to illuminate this “new direction”, which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831–1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a “free creation of the human spirit”3. They thus stand for an abstract perspective of mathematics in their entirety, described as ‘modern algebra’ in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on “general mathematical concepts” [allgemein-mathematische Begriffe]4, was the success of a cultural movement whose most important protagonists included Emmy Noether (1882–1935) and her pupil Bartel L. van der Waerden (1903–1996). With the use of the term ‘conceptual’, a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the “working and conceptual methods” [Arbeits- und Auffassungsmethoden]5 of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term “conceptual world” [Begriffswelt]6 in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

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Authors & Contributors
Parshall, Karen V. Hunger
Gray, Jeremy
McLarty, Colin
Vidal, J. Climent
Tur, J. Soliveres
Mehrtens, Herbert
Journals
Archive for History of Exact Sciences
NTM: Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin
Atti e Memorie, Accademia Nazionale di Scienze, Lettere e Arti, Modena
Historia Mathematica
Physis: Rivista Intemazionale di Storia della Scienza
Synthese
Publishers
American Mathematical Society
Princeton University Press
Birkhäuser
Indiana University
de Gruyter
Springer Spektrum
Concepts
Mathematics
Algebra
Set theory
Mathematical analysis
Arithmetic
Biographies
People
Dedekind, Richard
Noether, Emmy
Cantor, Georg Ferdinand Ludwig
Nekrasov, Pavel Alekseevich
Gregory, Duncan Farquharson
Kronecker, Leopold
Places
Germany
Russia
Italy
Japan
Great Britain
Times
19th century
20th century, early
17th century
Edo Era (Japan, 1603-1868)
18th century
Modern
Institutions
University of Chicago
Göttingen. Universität
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